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Relevant bibliographies by topics / Fourier decomposition

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Academic literature on the topic 'Fourier decomposition'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 June 2025

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Journal articles on the topic "Fourier decomposition"

1

Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.

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Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.

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Wang, Yanbo, and Tao Qian. "Adaptive Fourier decomposition in." Mathematical Methods in the Applied Sciences 42, no. 6 (2019): 2016–24. http://dx.doi.org/10.1002/mma.5494.

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ZHANG, LIMING, and HONG LI. "A NOVEL SIGNAL DECOMPOSITION APPROACH — ADAPTIVE FOURIER DECOMPOSITION." Advances in Adaptive Data Analysis 03, no. 03 (2011): 325–38. http://dx.doi.org/10.1142/s1793536911000702.

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This paper presents a novel signal decomposition approach — adaptive Fourier decomposition (AFD), which decomposes a given signal based on its physical characters. The algorithm is described in detail, that is based on recent theoretical studies on analytic instantaneous frequencies and stands as a realizable variation of the greedy algorithm. The principle of the algorithm gives rise to fast convergence in terms of energy. Effectiveness of the algorithm is evaluated by comparison experiments with the classical Fourier decomposition (FD) algorithm. The results are promising.

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Qian, Tao, Liming Zhang, and Zhixiong Li. "Algorithm of Adaptive Fourier Decomposition." IEEE Transactions on Signal Processing 59, no. 12 (2011): 5899–906. http://dx.doi.org/10.1109/tsp.2011.2168520.

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Kutay, M. Alper, Hakan Özaktaş, Haldun M. Ozaktas, and Orhan Arıkan. "The fractional Fourier domain decomposition." Signal Processing 77, no. 1 (1999): 105–9. http://dx.doi.org/10.1016/s0165-1684(99)00063-8.

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QIAN, TAO, and YANBO WANG. "REMARKS ON ADAPTIVE FOURIER DECOMPOSITION." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s0219691313500070.

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This is a continuation of the study of adaptive Fourier decomposition (AFD).15 Under a mild condition not in terms of smoothness, a convergence rate is provided. We prove that the selection of the parameters corresponding to Fourier series in the average sense is optimal. We also present the transformation matrices between the adaptive rational orthogonal system and the related sequence of the shifted Cauchy kernels and their derivatives.

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Qian, Tao. "Two-dimensional adaptive Fourier decomposition." Mathematical Methods in the Applied Sciences 39, no. 10 (2016): 2431–48. http://dx.doi.org/10.1002/mma.3649.

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Hansen, L., and J. O. Petersen. "Fourier Decomposition Parameters for the Halo RR Lyrae Variables U and V Caeli." International Astronomical Union Colloquium 82 (1985): 272–75. http://dx.doi.org/10.1017/s0252921100109509.

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AbstractUBVRI light curves are obtained for the two halo RR Lyrae variables U Caeli with period 0.420 days (73 observations) and V Caeli with period 0.571 days (42 observations). It is shown that their light curve characteristics are very similar to those of field RR Lyrae stars.Fourier decompositions are studied for all five magnitudes and the resulting amplitude ratios and phase differences are discussed. The differences in the Fourier decomposition parameters between the five magnitudes are shown to be relatively small. Comparisons of the Fourier decomposition parameters for the two halo RR Lyrae stars with recently published data for field RR Lyrae stars show no systematic differences.

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Kožar, Ivica, Željko Jeričević, and Tatjana Pecak. "Approximate modal analysis using Fourier decomposition." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012119. http://dx.doi.org/10.1088/1757-899x/10/1/012119.

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Dissertations / Theses on the topic "Fourier decomposition"

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Liu, Zhu Lin. "Speech synthesis via adaptive Fourier decomposition." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2493215.

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Li, Zhi Xiong. "A revision of adaptive Fourier decomposition." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2590642.

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Shi, Rong. "Applications of adaptive Fourier decomposition to financial data." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592936.

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Mai, Wei Xiong. "Time frequency distribution associated with adaptive Fourier decomposition and its variation." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2590643.

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Avetisyan, Zhirayr. "Mode decomposition and Fourier analysis of physical fields in homogeneous cosmology." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-107907.

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In this work the methods of mode decomposition and Fourier analysis of quantum fields on curved spacetimes previously available mainly for the scalar fields on Friedman-Robertson-Walker spacetimes are extended to arbitrary vector fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. Explicit constructions are performed for a variety of situations arising in homogeneous cosmology. A number of results concerning classical and quantum fields known for very restricted situations are generalized to cover almost all cosmological models.

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Blackburn, John William Teasdale. "High-resolution Fourier transform ion cyclotron resonance mass spectrometry and nuclear magnetic resonance spectroscopy of humic substances." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31149.

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Humic substances (HS) are described as a complex mixture of organic molecules formed by incomplete decomposition of plant, animal and microbial matter. They are found in soil, water and air and have many environmental roles, e.g. water retention and metal ion binding in soil. Despite their importance, the molecular composition of HS is poorly understood. This is mostly because of an inability to separate individual molecules from these complex mixtures and then characterise them by standard analytical methods such as NMR and MS. In order improve the understanding of these important mixtures I have studied them using a high-resolution analytical method, Fourier transform ion-cyclotron resonance mass spectrometry (FTICR MS). Initial efforts focussed on testing the, fast, automated data analysis of the large data sets produced. Two pieces of software were compared and the reliability of the formulae assigned by these was critically evaluated. This confident formula assignment was then applied to study the consequences of different ionisation and instrumental parameters on the mass spectra obtained. The use of laser desorption/ionisation (LDI) without the need to employ a matrix required in matrix assisted laser desorption/ionisation (MALDI) was explored. A comparison of LDI and electrospray ionisation (ESI) FTICR MS of natural organic matter samples showed that these methods ionise complementary sets of compounds. The LDI ionised compounds were characterised as aromatics or condensed aromatics and compounds belonging to lower oxygen classes (maximum number at O8), while ESI ionised higher oxygen classes (maximum number at O16) with a vast majority of compounds classified as aliphatic based on their modified aromaticity index. MALDI and LDI spectra produced very similar data with over 90% matching formulas implying that fragmentation is not caused by LDI, as taught previously. My work showed that to maximize the coverage by FTICR MS of the molecular space occupied by these complex mixtures, multiple ionization methods must be used. As a particularly convenient and readily deployable ionization technique, LDI should be included in standard analytical protocols for FTICR MS analysis of NOM. I have explored different parameters and experimental settings to obtain a fuller coverage of the molecular space of NOM, this showed that different experimental conditions enhance peak intensities in different m/z regions of the FTICR MS spectra and that information can be obtained outside of the narrow 200-700 m/z window. To gain chemical and structural information about humic substances beyond what is currently known, experiments aimed to label HS using different isotopes and at specific sites were developed and tested. Two methylation reactions were of particular interest. A methylation that selectively targeted carboxylic acid groups and incorporated deuterium in the form of CD3 groups. An international standard, Suwannee River fulvic acid, was methylated and analysed by high-resolution mass spectrometry in order to gain information on the number and distribution carboxylic acid groups. This proved challenging due to the reactivity of the unknown molecules being difficult to determine in advance. Additionally, the peak separation being reduced to as low as 1.5 mDa pushed the instrument resolution and assignment confidence to their limits. The second methylation method explored used 13CH3I, a nonselective agent reacting with any labile proton, particularly attaching 13CH3 groups to carboxylic, phenolic and alcoholic OH groups. I prepared a methylated sample of fulvic acid from a Red Moss raised bog (Balerno, near Edinburgh) ready for analyses by high field NMR. This investigation yielded structures of a number of phenolic compounds for the first time by NMR.

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Liu, Xiaohua. "Anion-Peptide Adduct Formation and Decomposition As Studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) Mass Spectrometry." ScholarWorks@UNO, 2013. http://scholarworks.uno.edu/td/1748.

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A new “best match” match model has been developed to account for adduct formation on multiply charged peptides observed in negative ion electrospray mass spectrometry. To obtain a stable adduct, the model necessitates an approximate matching of apparent gas-phase basicity (GBapp) of a given proton bearing site on the peptide with the gas-phase basicity (GB) of the anion attaching at that site. Evidence supporting the model is derived from the fact that singly charged adducts were only observed for lower GB anions: HSO4-, I-, CF3COO-. Ions that have medium GBs (NO3-, Br-, H2PO4-) only form adducts having -2 charge states, whereas Cl- (higher GB) can form adducts having -3 charge states. Hydrogen bonds are the main interactions pertinent to the “Best Match” model, however, ion-ion interactions formed between peptides ([Glu]Fibrinopeptide B, Angiotensin I or [Asn1,Val5]-Angiotensin II) and low GB anions (ClO4- or HSO4-) have been established by CID-MS/MS. Evidence for ion-ion interactions comes especially from product ions formed during the first dissociation step, where, in addition to the expected loss of the anion or neutral acid, other product ions that require covalent bond cleavage (i.e., H2O or NH3 loss) are also observed. In this study, the “Best Match” model is further supported by the decomposition behavior of adducts formed when Na+/H+ exchange has occurred on peptides. Na+/H+ exchanges were found to occur preferentially at higher acidity sites. Without any Na+/H+ exchange, F- and CH3COO- can hardly form observable adducts with [Glu]Fibrinopeptide B. However, after multiple Na+/H+ exchanges, F- and CH3COO- do form stable adducts. This phenomenon can be rationalized by considering that Na+ cations serve to “block” the highly acidic sites, thereby forcing them to remain overall neutral. This leaves the less acidic protons available to match with higher GB anions. According to the "best match" model, high GB anions will match with high GBapp sites on the peptide, whereas low GB anions will match with low GBapp peptide sites. High charge states readily augment GBapp of the peptide (through-space effect). Na+/H+ exchanges substantially decrease GBapp by neutralizing charged sites, while slightly increasing intrinsic GBs by the inductive effect.

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Workalemahu, Tsegaselassie. "Singular Value Decomposition in Image Noise Filtering and Reconstruction." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/52.

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The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods assume that the images have been degraded by the application of a blurring function and the addition of noise. Finally, we present numerical experiments for the SVD restoration and compression to evaluate our computation.

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Eliasson, Bengt. "Numerical Vlasov–Maxwell Modelling of Space Plasma." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2929.

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The Vlasov equation describes the evolution of the distribution function of particles in phase space (x,v), where the particles interact with long-range forces, but where shortrange "collisional" forces are neglected. A space plasma consists of low-mass electrically charged particles, and therefore the most important long-range forces acting in the plasma are the Lorentz forces created by electromagnetic fields. What makes the numerical solution of the Vlasov equation a challenging task is that the fully three-dimensional problem leads to a partial differential equation in the six-dimensional phase space, plus time, making it hard even to store a discretised solution in a computer’s memory. Solutions to the Vlasov equation have also a tendency of becoming oscillatory in velocity space, due to free streaming terms (ballistic particles), in which steep gradients are created and problems of calculating the v (velocity) derivative of the function accurately increase with time. In the present thesis, the numerical treatment is limited to one- and two-dimensional systems, leading to solutions in two- and four-dimensional phase space, respectively, plus time. The numerical method developed is based on the technique of Fourier transforming the Vlasov equation in velocity space and then solving the resulting equation, in which the small-scale information in velocity space is removed through outgoing wave boundary conditions in the Fourier transformed velocity space. The Maxwell equations are rewritten in a form which conserves the divergences of the electric and magnetic fields, by means of the Lorentz potentials. The resulting equations are solved numerically by high order methods, reducing the need for numerical over-sampling of the problem. The algorithm has been implemented in Fortran 90, and the code for solving the one-dimensional Vlasov equation has been parallelised by the method of domain decomposition, and has been implemented using the Message Passing Interface (MPI) method. The code has been used to investigate linear and non-linear interaction between electromagnetic fields, plasma waves, and particles.

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Colom, i. Bernadich Miquel. "Measuring the Characteristic Sizes of Convection Structures in AGB Stars with Fourier Decomposition Analyses : the Stellar Intensity Analyzer (SIA) Pipeline." Thesis, Uppsala universitet, Teoretisk astrofysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414041.

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Context. Theoretical studies predict that the length scale of convection in stellar atmospheres isproportional to the pressure scale height, which implies that giant and supergiant stars should have convection granules of sizes comparable to their radii. Numerical simulations and the observation of anisotropies on stellar discs agree well with this prediction. Aims. To measure the characteristic sizes of convection structures of models simulated with the CO5BOLD code, to look at how they vary between models and to study their limitations due to numerical resolution. Methods. Fourier analyses are performed to frames from the models to achieve spatial spectral power distributions which are averaged over time. The position of the main peak and the averagevalue of the wavevector are taken as indicators of these sizes. The general shape of the intensity map of the disc in the frame is fitted and subtracted so that it does not contaminate the Fourier analysis. Results. A general relationship of the convection granule size being more or less ten times larger than the pressure length scale is found. The expected wavevector value of the time-averaged spectral power distributions is higher than the position of the main peak. Loose increasing trends with the characteristic sizes by the pressure scale height increasing against stellar mass, radius, luminosity,temperature and gravity are found, while a decreasing trends are found with the radius and modelresolution. Bad resolution subtracts signals on the slope at the side of the main peak towards larger wavevector values and in extreme cases it creates spurious signal towards the end of the spectrum due to artifacts appearing on the frames. Conclusions. The wavevector position of the absolute maximum in the time-averaged spectral power distribution is the best measure of the most prominent sizes in the stellar surfaces. The proportionality constant between granule size and pressure length scale is of the same order ofmagnitude as the one in the literature, however, models present sizes larger than the ones expected, likely because the of prominent features do not correspond to convection granules but to larger features hovering above them. Further studies on models with higher resolution will help in drawing more conclusive results. Appendix. The SIA pipeline takes a set of time-dependent pictures of stellar disks and uses a Fourier Analysis to measure the characteristic sizes of their features and other useful quantities, such as standard deviations or the spatial power distributions of features. The main core of the pipeline consists in identifying the stellar disc in the frames and subtracting their signal from the spatial power distributions through a general fit of the disc intensity. To analyze a time sequence, the SIA pipeline requires at least two commands from the user. The first commandorders the SIA pipeline to read the .sav IDL data structure file where the frame sequence is stored and to produce another .sav file with information on the spectral power distributions, the second command orders the reading of such file to produce two more .sav files, one containing time-averaged size measurements and their deviations while the other breaking down time-dependant information and other arrays used for the calculations. The SIA pipeline has been entirely written in Interactive Data Language (IDL). Most of the procedures used here are original from the SIA pipeline, but a small handfull like ima3_distancetransform.pro, power2d1d.pro, extremum.pro and smooth2d.pro from Bernd Freytag and peaks.pro and compile opt.pro amongst others are actually external.<br><p>The report consists in two parts:</p><p>1.- The main project, where we apply our pipeline and get scientific results.</p><p>2.- The appendix, where a technical description of the pipeline is given.</p>

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Books on the topic "Fourier decomposition"

1

Moin, Parviz. Characteristic eddy decomposition of turbulence in a channel. National Aeronautics and Space Administration, Ames Research Center, 1991.

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Golubov, B., V. Skvortsov, and A. Efimov. Walsh Series and Transforms: Theory and Applications. Springer Netherlands, 2012.

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Bisseling, Rob H. Parallel Scientific Computation. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788348.001.0001.

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This book explains how to use the bulk synchronous parallel (BSP) model to design and implement parallel algorithms in the areas of scientific computing and big data. Furthermore, it presents a hybrid BSP approach towards new hardware developments such as hierarchical architectures with both shared and distributed memory. The book provides a full treatment of core problems in scientific computing and big data, starting from a high-level problem description, via a sequential solution algorithm to a parallel solution algorithm and an actual parallel program written in the communication library BSPlib. Numerical experiments are presented for parallel programs on modern parallel computers ranging from desktop computers to massively parallel supercomputers. The introductory chapter of the book gives a complete overview of BSPlib, so that the reader already at an early stage is able to write his/her own parallel programs. Furthermore, it treats BSP benchmarking and parallel sorting by regular sampling. The next three chapters treat basic numerical linear algebra problems such as linear system solving by LU decomposition, sparse matrix-vector multiplication (SpMV), and the fast Fourier transform (FFT). The final chapter explores parallel algorithms for big data problems such as graph matching. The book is accompanied by a software package BSPedupack, freely available online from the author’s homepage, which contains all programs of the book and a set of test programs.

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Time‒Frequency and Time‒Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling (Applied and Numerical Harmonic Analysis). Birkhäuser Boston, 2007.

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Book chapters on the topic "Fourier decomposition"

1

Roepstorff, Gert. "Fourier Decomposition." In Path Integral Approach to Quantum Physics. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57886-1_4.

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Chen, Hsin-Chu. "A Block Fourier Decomposition Method." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-48051-x_35.

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Zhou, Wei, Zhongren Feng, Y. F. Xu, Xiongjiang Wang, and Hao Lv. "Empirical Fourier Decomposition for Time-Domain Signal Decomposition." In Topics in Modal Analysis & Testing, Volume 8. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75996-4_8.

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He, Can, Liming Zhang, Xiangjian He, and Wenjing Jia. "A New Image Decomposition and Reconstruction Approach – Adaptive Fourier Decomposition." In MultiMedia Modeling. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14442-9_20.

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Petersen, J. O. "On the Application of Fourier Decomposition Parameters." In Nonlinear Phenomena in Stellar Variability. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1062-4_20.

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Tilmanne, Joelle, and Thierry Dutoit. "Stylistic Walk Synthesis Based on Fourier Decomposition." In Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03892-6_9.

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Simon, Norman R. "The Fourier Decomposition Technique: Interpreting the Variations of Pulsating Stars." In Pulsation and Mass Loss in Stars. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3029-2_2.

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Tan, Chunyu, Liming Zhang, and Tao Qian. "A New Supervised Learning Approach: Statistical Adaptive Fourier Decomposition (SAFD)." In Communications in Computer and Information Science. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-36802-9_42.

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Masliev, I. "Use of a Fourier Decomposition Technique in Aquatic Ecosystems Modelling." In Predictability and Nonlinear Modelling in Natural Sciences and Economics. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0962-8_34.

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Hussein, Hagar, Ashhadul Islam, and Samir Brahim Belhaouari. "Stress Detection Using Novel Time–Frequency Decomposition: Progressive Fourier Transform." In Springer Proceedings in Mathematics & Statistics. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-4876-1_16.

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Conference papers on the topic "Fourier decomposition"

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Hassan, Umaisa, and Amit Singhal. "Neural Network-Based Schizophrenia Diagnosis Utilizing Fourier Decomposition." In 2024 Global Conference on Communications and Information Technologies (GCCIT). IEEE, 2024. https://doi.org/10.1109/gccit63234.2024.10862502.

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Long, Ruiqi, Hongyi Xie, and Defu Lian. "Time Series Forecasting with Multi-scale Decomposition and Fourier Neural Operators." In 2024 7th International Conference on Computer Information Science and Application Technology (CISAT). IEEE, 2024. http://dx.doi.org/10.1109/cisat62382.2024.10695364.

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Li, Hao, Ziyuan Zhan, Zhizhuo Zhang, Zhiming Yang, Liang Bao, and Mouxun Sun. "Modeling Method of Coaxial Cable Transmission Characteristics Based on Fourier Decomposition." In 2024 IEEE 2nd International Conference on Electrical, Automation and Computer Engineering (ICEACE). IEEE, 2024. https://doi.org/10.1109/iceace63551.2024.10898676.

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Shen, Jianhao, Daniel Donnelly, Asela Perera, and Swapnajit Chakravarty. "Phase-change-material integrated, phase-error corrected, resolution-enhanced Michelson Interferometer Fourier Transform Spectrometer." In CLEO: Science and Innovations. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_si.2024.sf2a.6.

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We experimentally demonstrate a hybrid silicon waveguide integrated with phase change materials to enable active phase error correction for spectral decomposition in compact on-chip Fourier Transform spectrometer based on spatially heterodyned array of Michelson interferometers.

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Mahato, Ashok, Shailesh Vitthalrao Bhalerao, Ram Bilas Pachori, Vikram M. Gadre, and Dipika Das Mahapatra. "Neurological Responses to Meditation with EEG Analysis Using Novel Empirical Fourier-Bessel Decomposition Approach." In 2025 10th International Conference on Signal Processing and Communication (ICSC). IEEE, 2025. https://doi.org/10.1109/icsc64553.2025.10968250.

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Ding, Hong, Chia Chao Kang, SuYang Xi, Zehang Liu, Xuan Zhang, and Yi Ding. "FPGA-Optimized Hardware Accelerator for Fast Fourier Transform and Singular Value Decomposition in AI." In 2024 International Conference on Computing Innovation, Intelligence, Technologies and Education (CIITE). IEEE, 2024. https://doi.org/10.1109/ciite62244.2024.10987675.

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Melli, F., K. Vasko, L. Rosa, F. Benabid, and L. Vincetti. "Transverse Roughness: Modeling and Effects Analysis on Inhibited Coupling Fibers." In Specialty Optical Fibers. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/sof.2024.som3f.6.

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A Transverse Roughness theoretical model based on the Azimuthal Fourier Decomposition is proposed to analyse the effects of this perturbation on the Confinement Loss of Hollow-Core Inhibited Coupling Fibers. Scaling laws are also given.

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Brault, Janes W., and Mark C. Abrams. "DECOMP: A Fourier Transfom Spectra Decomposition Program." In High Resolution Fourier Transform Spectroscopy. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/hrfts.1989.pdp2.

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Current techniques for processing high resolution Fourier transform spectra revolve around interactive graphical display of the spectrum on a computer. The DECOMP spectrum decomposition program is designed explicitly for the reduction of Fourier transform spectra and focuses on reducing a spectrum into a list of line parameters. Basic methods of spectrum manipulation will be demonstrated and a IBM PC - compatible computer will be available for hands-on demonstrations of the process of spectrum analysis. Figures 1 and 2 illustrate the process of background subtraction: in Figure 1 a low resolution spectrum is generated by binning the high resolution spectrum and beneath the spectrum is a background correction function generated by creating a low resolution "minima" spectrum and smoothing the spectrum. The results of the background correction are given in Figure 2. Figure 3 illustrates a common problem in Fourier transform spectroscopy: the finite length of the interferogram introduces "ringing" into the spectrum. Using a filtered fitting routine in DECOMP the ringing can be effectively removed yielding a spectrum illustrated in Figure 4, in which several new spectral features that had been hidden beneath the ringing. An example of the atlas plots that can be generated using DECOMP is given in Figure 5.

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Goyal, Navin, Santosh Vempala, and Ying Xiao. "Fourier PCA and robust tensor decomposition." In STOC '14: Symposium on Theory of Computing. ACM, 2014. http://dx.doi.org/10.1145/2591796.2591875.

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Borowicz, Adam. "GPU Implementation of Adaptive Fourier Decomposition." In 2019 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA). IEEE, 2019. http://dx.doi.org/10.23919/spa.2019.8936752.

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